To do after the break (for Lynn)

[lengelberts]

To do:

• [x] Adapt hecke_operator_on_qexp such that it returns a power series up to the correct precision.
• [x] Complete tests for eisenstein_series_poly, eisenstein_series_qexp, the generators, and victor_miller_basis.
• [x] Write function for eta-product/-quotient.
• [x] Improve big_oh.
• [x] Extend the functions delta_poly, delta_qexp, eisenstein_series_poly, and eisenstein_series_qexp such that they work for all rings (instead of only ZZ or QQ, resp.). NOTE: then need to adapt tests!
• [x] Extend the functions hecke_operator_on_qexp and hecke_operator_on_basis to the space of all modular forms (instead of only cusp forms).

In addition, fix (currently not working as it should):

• [x] hecke_operator_on_qexp for n = 1. Currently only returns 1. PROBLEM. (For now, test commented so that tests keep running.)
• [x] victor_miller_basis now returns an array consisting of fmpq_rel_series elements instead of fmpz_rel_series.

Check comments in files:

• [ ] Check Sage implementation of hecke_operator_on_basis.
• [ ] Comment about prec in eisenstein_series_qexp. How do we define prec for the PowerSeriesRing? NOTE: In each function where we define a PowerSeriesRing I have used the input argument prec. So if need to update, also need to check the other files if need to change.

Other:

• Update README.md.
• Update LICENSE.md.
• Create a .travis.yml file.
• Continue setting up as a module (see below for relevant sources).
• Running tests now takes very long. It might be good to look for a way to optimise it.

Sources about setting up as a module and testing

• http://abelsiqueira.github.io/blog/automated-testing/
• http://www.stochasticlifestyle.com/finalizing-julia-package-documentation-testing-coverage-publishing/

[lengelberts]

1 and 7 fixed and informally tested, but still need to write tests

[lengelberts]

Point 6 fixed by commit 6274304f3393448edc0dd5cfaa373e59f4f95e1c. However, need to check.

Point 5 fixed for delta by commit 243175d0b521df3023a5c804e01eb10862d8e3fe. Not yet fixed for eisenstein. The reason that eisenstein returns a QQ poly or power series is also the reason why victor_miller_basis returns an fmpq series instead of fmpz... (Point 8)

[lengelberts]

Point 5 fixed now also for eisenstein by commits cba7504224ad5ca417c4dfdf3b1dbfa9a3e702dd and f8f8c96887bd0edc754775d7df0e3d5d12877c43. Note that K will automatically be QQ if normalization is linear or constant.

[lengelberts]

To do in the coming days (points 2, 3, 4, 8):

• [ ] Rewrite functions so that only delta_qexp uses big_oh.

• [x] Adapt victor_miller_basis so that it has cusp_only as additional input and can return a basis for both the cuspidal subspace as modular.

• [x] Adapt victor_miller_basis so that it returns an array consisting of fmpz_rel_series elements.

• [ ] Complete tests.

• [x] Write eta_quotient function.

• [ ] Benchmarking.

For later (issues):

• Output of eisenstein_series_poly and eisenstein_series_qexp in QQ if normalization is "linear" or "constant". Want to change?

• Is there an alternative for big_oh?

• Is there an alternative for divisors?

[aghitza]

There are optimisations (and a change of name) for big_oh in commit e45e26dfe33d068184ee15c91c19e4162105a4fc